Limits & Continuity Questions and Answers

10 ST For h t 4e 03t cos 2t in Ex 87 1 what is the minimum value of t for which h t damps out to values less than or equal to 1 Select one 3 63 3 23 x Incorrect 3 53

Example 43 2 Using the figure shown find a f h 4 b fh 4 c h f 4 solution Be observant and keep up with which function is which Assume outputs are integers Start by finding f 4 and h 4 f 4 5 h 4 1 a f 4 h 4 5 1 6 b f 4 h 4 5 1 5 c h f 4 h 5 2 10 Type answer as an integer no decimals 5 Help Lecture 43 Ex 43 2 16 Using the figure in Problem 15 find f g 7 43 10 f x h x

14 Leth be the function defined by h t 9sin 8t 12 A maximum value of his attaine at which of the following values of t A T1 2 B 4 C 1 8 Select one OA D 16

lim x 1 1 n 1 x 1 where e e sin xx 100 2 72x 1 5050 3 n 100 is equal to 5050 4 4950 t

Help Lecture 84 Ex 84 1 114 Split Rock Lighthouse in Minnesota rests atop a 130 tall cliff Use the dimensions shown to find h the height of the lighthouse rounded to the nearest foot 130 Wikipedia Creative Commons image by Jim Sorbie 319 30 0 22 3

Graph f z log 2 below First locate the vertical a EE 6 5 4 why 3 27 8 7 6 5 4 3 2 1 723 2 3 1 2 3 4 5 6 7 8

Red Blue e Green Q Match each equation with a graph above In x log x Black a black b blue c green

decimals Help Lecture 43 Ex 43 1 15 The figure shows the complete graphs of f and g Based on the graphs the equatio f g x 0 has how many roots g x 10 10 8 6 f x 3 10

The Narnia Postal Service charges more for boxes whose combined length and girth exceeds 42 in The length of a package is the length of its longest side the girth is the perimeter of the cross section 2w 2h What is the maximum volume of a package with a square cross section w h that does not exceed the 42 in standard in help numbers Maximum volume V 2744

fx B C Formula Add Subtract Cell Referencing Prepare a Partial Income Statement PROBLEM hy provides the following information for the mon 022

376 A ship traveling through Cape Horn recorded a wave height of 9 m and an averag period of 13 2 s The tide height was 0 5 m relative to mean sea level Which of th following trig functions is a good representation of these wave conditions elect one A B A h t 13 2 sin B h t 4 5 sin 2 9 t 0 5 2 13 2 0 5 C h t 0 5sin t D h t 4 5 sin 13 2t 0 5 13 2

decimals with one space between the number and the units For example 387 mi 415 mi Help Lecture 79 Ex 79 2 12 Find the distance between Tierra del Fuego and the Nordenskjold Coast of Antarctic Round to the nearest mile Nordonckjald Coast 850 mi Tierra del Fuego 56 1 415 mi

11 Which of the following is an equation of an ellipse A 3x y 2 0 B x y 12x 4y 2 0 C 3x 12x 4y 2 0 D 3x y 12x 4y 2 0 E 3x 3y 12x 4y 2 0 Select one A B C D E O

1740 The graph of the function f and a table of values for the function g are shown Find f g 5 X 2 1 0 1 2 3 4 5 6 g x 3 4 2 1 4 5695 10 15 ty

ecimals no units lelp Lecture 86 Ex 86 1 66 Sailing To maintain a close reach while sailing into a southerly headwind the c used the following function to vary between port and starboard tacks h t 175 5 3 sin 11 degrees If t is in hours find the ship s heading after 9 hours No GC

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Find the exact value of cos u v given that sin u 5 3 5 with u in quadrant III and sin v 13 cos u v Simplify your answer Type an integer or a simplified fraction with v in the quadrant I

Find a power series representation for the function f x 2 x and determine the interval of convergence Show work and explain your steps

Activity 8 4 7 For a j use appropriate tests to determine the convergenc or divergence of the following series Throughout if a series is a convergent geometric series find its sum a b C e d f IM8 IM8 IM8 IM8 IM8 IM8 IM8 IM IM g h k 0 i 2 k 2 k 1 2k 2k 1 k k 1 100 k 2k 5k k 1 k5 1 3k 1 7k 2 1 1 k 1 k 1 k 1 A

1 point A 1 3 5 B 2 3 Check ALL elements of the following sets a An B A 5 B 2 C 1 D 3 E 4 b AUB DA 3 B 5 C 1 D 4 E 2 c A B DA 3 B 2 C 5 D 4 E 1

point The sets A and B are such that A 10 B 20 The largest possible value of AU B is The smallest possible value of AU B is The largest possible value of A n Bis The smallest possible value of An Bis The value of AN B AU B is

Suppose that A 2 4 6 B 2 6 C 4 6 and D 4 6 8 Determine which of these se are subsets of which other of these sets Check ALL correct answers below OA CCD OB ACC C DCA D CCA OE BCC F BCD G ACD H BCA

Functions f x x 1 f 1 x x 1 x 0 a Find the domains of f and f 1 Enter your answers using interval notation domain of f domain of f 1 b Find the ranges of f and f 1 Enter your answers using interval notation range of f Point 2 1 1 2 range of f 1 c Show that the slopes of the graphs of f and f 1 are reciprocals at the given points f 2 f 1

Question 28 6 Part 3 of 3 he equation governing the amount of current I in amperes after time t in second E in volts is I R e R L 1 e Iso to obtain

Find the radius of convergence for 5x k 1 a 5 c 15 b d 1 0

a b c d Find Ma 2 2 1 2x 2x 1 3 1 2x 2 21 1 2x x 2 3 2 4 x x 3 2 2

etermine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0 001 f x sin x approximate f 0 5

Cost of Paint The first coat of paint for the outside walls of a building requires 1 l of paint for eaen 10m of wall Surface The Second Coat requires II for every 15m If the paint cost 3 50 per liter what will be the cost of two coats of paint for the four outside walls of a rectangul building 20m long 15 m wide and 6m high J Gebumu

This question has two parts Answer he first part correctly to get the second part Suppose you have a function f x whose average rate of change is always a constant number c That is suppose f x f a x a Rearrange this relationship to get f x alone on one side of the equals sign f x c x a f a c for all inputs a and x OF Part 2 of 2 Note that if we write this as f x cx f a ac then f a ac is just a number Average rate of change Using other symbols we could use m to stand for c and b to stand for f a ac then the relationship can be written f x mx b This is what is known as a linear function Now suppose you have any linear function f x mx b and any two inputs a and x What number do you get for the average rate of change of f x on the interval a x

4 A rectangular bu 80m is surroun 2 5m wide

the given function f to answer parts a through f below x 4 log x 2 Find the domain of f domain of f is 2 00 e your answer in interval notation Choose the correct graph of f below AY Q xQ C From the graph determine the range and any asymptotes of f range of f is 00 00 be your answer in interval notation Question 20 6 4 83 Part 4 of 8 Q Q

e given function f to answer parts a through f below 4 log5 x 2 nd the domain of f Q

ulator to evaluate the expression In 6 3 log 6

Find the domain of the function x 8 X g x log g The domain is

Find the domain of the function 7 X f x 5 5 log 85 The domain off is 0 notation

1 x 8 Given f x on the interval 10 10 h Your answer will be an expression involving h 2 find the average rate of change of f x

For the graph below determine if it represents a function that is increasing or decreasing and whether the function is concave up or concave down Select an answer Select an answer

ENTERING INTERVAL ANSWERS For intervals of values enter your answer using interval notation Here are some examples of how interval notation relates to inequalities Inequality Interval Notation 3 5 3 5 x 3 3 3 x 5 or 7 x 9 3 5 U 7 9 3 x 5 3 x 5 With inequalities we use less than or greater than to exclude the endpoint of the interval With interval notation we use use round parentheses or With inequalities we use less than or equal to or greater than or equal to to include the endpoint of the interval With interval notation we use use square brackets or To combine two intervals use U an uppercase letter u for union U Use oo two lowercase letter o s for infinity For example to enter 2 U 3 6 you would type 00 2 U 3 6 Try it now Enter the interval equivalent to 2 x 5 or x 7

22 In an arithmetic sequence a 42 and a 117 What is ase

B a If all the graphs above have equations with form y Which graph has the largest value for b Select an answ Which graph has the smallest value for b Select an ans Which graph has the largest value for a Select an answ Question Help Video Message instructor

K B 0 R G Q Match each equation with a graph above 4 1 59 4 1 17 4 0 89 4 0 71 a orange 0 b black K c red R d blue B

R 2 atch each equation with a graph above 2 2 22 B 2 Q a red R b green G c orange 0 d blue B

K The human resources director for a c numbers of applications from people

Give the domains of the following functions in interval notation f x 5 x 10 Domain g x main 3 2x 8

Given the function g m m 4 Evaluate g 5 Solve g m 2 1 OT

Evaluate the limit using L Hopital s rule lim 15a esz

Evaluate the following limit 2x tan 4x lim 2 0 5x tan 2x Enter Inf if your answer is co enter Inf if your answer is oo and enter DNE if ta

Evaluate the limit using L Hospital s rule if necessary lim 21 0 sin x

Evaluate the limit using L Hospital s rule sin 9x lim 2 0 tan 82

Evaluate the limit using L Hospital s rule if necessary e 1 lim 20 sin 4x